OFFSET
0,2
COMMENTS
Central coefficients of number triangle A115268.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 2, -4, 2, 0, -1, 2, -1).
FORMULA
G.f.: (1+x^4)/((1-x)^2*(1-x^4)^2).
a(n) = sum{k=0..n, floor((k+4)/2)^2}.
a(n) = A115268(2n, n).
a(n) = 2*a(n-1)-a(n-2)+2*a(n-4)-4*a(n-5)+ 2*a(n-6)- a(n-8)+2*a(n-9)-a(n-10) with a(0)=1, a(1)=2, a(2)=3, a(3)=4, a(4)=8, a(5)=12, a(6)=16, a(7)=20, a(8)=29, a(9)=38. - Harvey P. Dale, Jun 07 2011
a(n) = (2*n^3+18*n^2+61*n+75+3*(n+3)*(-1)^n+6*(n+4-(n+2)*(-1)^n)*(-1)^((2*n-1+(-1)^n)/4))/96. - Luce ETIENNE, Mar 17 2015
MATHEMATICA
Accumulate[Table[Floor[(n+4)/4]^2, {n, 0, 50}]] (* or *) LinearRecurrence[ {2, -1, 0, 2, -4, 2, 0, -1, 2, -1}, {1, 2, 3, 4, 8, 12, 16, 20, 29, 38}, 50] (* Harvey P. Dale, Jun 07 2011 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 18 2006
STATUS
approved